Applied Mathematics and Mechanics

, Volume 40, Issue 9, pp 1239–1254 | Cite as

Effects of nozzle and fluid properties on the drop formation dynamics in a drop-on-demand inkjet printing

  • A. B. Aqeel
  • M. Mohasan
  • Pengyu LvEmail author
  • Yantao YangEmail author
  • Huiling Duan


The droplet formation dynamics of a Newtonian liquid in a drop-on-demand (DOD) inkjet process is numerically investigated by using a volume-of-fluid (VOF) method. We focus on the nozzle geometry, wettability of the interior surface, and the fluid properties to achieve the stable droplet formation with higher velocity. It is found that a nozzle with contracting angle of 45° generates the most stable and fastest single droplet, which is beneficial for the enhanced printing quality and high-throughput printing rate. For this nozzle with the optimal geometry, we systematically change the wettability of the interior surface, i.e., different contact angles. As the contact angle increases, pinch-off time increases and the droplet speed reduces. Finally, fluids with different properties are investigated to identify the printability range.

Key words

inkjet printing drop-on-demand (DOD) droplet formation nozzle geometry surface wettability printability range 



density (kg·m-3)


pressure (Pa)


dynamic viscosity (Pa · s)


surface tension (N · m-1)


droplet velocity (m · s-1)


gravitational acceleration (m · s-2)


curvature of gas-liquid interface


nozzle wall contact angle (°)


nozzle contracting angle (°)


pinch-off speed (m · s-1)


volume fraction of gas phase


nozzle diameter (m)


primary pinch-off time (s)


end pinch-off time (s).

Chinese Library Classification


2010 Mathematics Subject Classification



Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.



A. B. AQEEL would like to thank the Chinese Scholarship Council (CSC) for providing Chinese Government Scholarship (CGS).


  1. [1]
    YUZO, I., SHINJI, K., YOSHIMITSU, A., and YASUHIRO, A. Inkjet fabrication of polymer microlens for optical-i/o chip packaging. Japanese Journal of Applied Physics, 39(3B), 1490–1493 (2000)Google Scholar
  2. [2]
    BERG, M. V. D., SMITH, P. J., PERELAER, J., SCHROF, W., KOLTZENBURG, S., and SCHUBERT, U. S. Inkjet printing of polyurethane colloidal suspensions. Soft Matter, 3(2), 238–243 (2007)Google Scholar
  3. [3]
    STRINGER, J. and DERBY, B. Limits to feature size and resolution in inkjet printing. Journal of the European Ceramic Society, 29(5), 913–918 (2009)Google Scholar
  4. [4]
    WIJSHOFF, H. The dynamics of the piezo inkjet printhead operation. Physics Reports, 491(4), 77–177 (2010)Google Scholar
  5. [5]
    ASTRE JON-PITA, J. R., BAXTER, W. R. S., MORGAN, J., TEMPLE, S., MARTIN, G. D., and HUTCHINGS, I. M. Future, opportunities and challenges of inkjet technologies. Atomization and Sprays, 23(6), 1490–1493 (2013)Google Scholar
  6. [6]
    BOS, A. V. D., MEULEN, M. J. V. D., DRIESSEN, T., BERG, M. V. D., REINTEN, H., WIJSHOFF, H., VERSLUIS, M., and LOHSE, D. Velocity profile inside piezoacoustic inkjet droplets in flight: comparison between experiment and numerical simulation. Physical Review Applied, 1(1), 0140041 (2014)Google Scholar
  7. [7]
    HE, B., YANG, S., QIN, Z., WEN, B., and ZHANG, C. The roles of wettability and surface tension in droplet formation during inkjet printing. Scientific Reports, 7(1), 11841 (2017)Google Scholar
  8. [8]
    DERBY, B. Inkjet printing of functional and structural materials: fluid property requirements, feature stability, and resolution. Annual Review of Materials Research, 40(1), 395–414 (2010)Google Scholar
  9. [9]
    BASARAN, O. A., GAO, H., and BHAT, P. P. Nonstandard inkjets. Annual Review of Fluid Mechanics, 45(1), 85–113 (2013)zbMATHGoogle Scholar
  10. [10]
    MARTIN, G. D., HOATH, S. D., and HUTCHINGS, I. M. Inkjet printing —the physics of manipulating liquid jets and drops. Journal of Physics: Conference Series, 105(1), 012001 (2008)Google Scholar
  11. [11]
    LIOU, T. M., CHAN, C. Y., and SHIH, K. C. Effects of actuating waveform, ink property, and nozzle size on piezoelectrically driven inkjet droplets. Microfluidics and Nanofluidics, 8(5), 575–586 (2010)Google Scholar
  12. [12]
    RAYLEIGH, L. On the instability of jets. Proceedings of the London Mathematical Society, 10, 4–13 (1878)MathSciNetzbMATHGoogle Scholar
  13. [13]
    SAVART, F. Memoire sur la constitution des veines liquides lancées par des orifices circulaires en mince paroi. Annales de Chimie et de Physique, 53, 337–386 (1833)Google Scholar
  14. [14]
    RAYLEIGH, L. On the instability of a cylinder of viscous liquid under capillary force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, 34(207), 145–154 (1892)zbMATHGoogle Scholar
  15. [15]
    PIMBLEY, W. T. and LEE, H. C. Satellite droplet formation in a liquid jet. IBM Journal of Research and Development, 21(1), 21–30 (1977)Google Scholar
  16. [16]
    YUEN, M. C. Non-linear capillary instability of a liquid jet. Journal of Fluid Mechanics, 33(1), 151–163 (1968)zbMATHGoogle Scholar
  17. [17]
    EGGERS, J. Nonlinear dynamics and breakup of free-surface flows. Reviews of Modern Physics, 69(3), 865–930 (1997)zbMATHGoogle Scholar
  18. [18]
    NOTZ, P. K., CHEN, A. U., and BASARAN, O. A. Satellite drops: unexpected dynamics and change of scaling during pinch-off. Physics of Fluids, 13(3), 549–552 (2001)zbMATHGoogle Scholar
  19. [19]
    DONG, H., CARR, W. W., and MORRIS, J. F. Visualization of drop-on-demand inkjet: drop formation and deposition. Review of Scientific Instruments, 77(8), 085101 (2006)Google Scholar
  20. [20]
    DONG, H., CARR, W. W., and MORRIS, J. F. An experimental study of drop-on-demand drop formation. Physics of Fluids, 18(7), 072102 (2006)Google Scholar
  21. [21]
    CASTRE JON-PITA, J. R., MARTIN, G. D., HOATH, S. D., and HUTCHINGS, I. M. A simple large-scale droplet generator for studies of inkjet printing. Review of Scientific Instruments, 79(7), 075108 (2008)Google Scholar
  22. [22]
    FAN, K. C, CHEN, J. Y., WANG, C. H., and PAN, W. C. Development of a drop-on-demand droplet generator for one-drop-fill technology. Sensors and Actuators A: Physical, 147(2), 649–655 (2008)Google Scholar
  23. [23]
    KWON, K. S. Speed measurement of ink droplet by using edge detection techniques. Measurement, 42(1), 44–50 (2009)Google Scholar
  24. [24]
    MATHUES, W., MCILORY, C, HARLEN, O. G., and CLASEN, C. Capillary breakup of suspensions near pinch-off. Physics of Fluids, 27(9), 093301 (2015)Google Scholar
  25. [25]
    FROMM, J. E. Numerical calculation of the fluid dynamics of drop-on-demand jets. IBM Journal of Research and Development, 28(3), 322–333 (1984)Google Scholar
  26. [26]
    ADAMS, R. L. and ROY, J. A one-dimensional numerical model of a drop-on-demand inkjet. Journal of Applied Mechanics, 53(1), 193–197 (1986)Google Scholar
  27. [27]
    REIS, N. and DERBY, B. Inkjet deposition of ceramic suspensions: modeling and experiments of droplet formation. Material Research Society Proceedings, 625, 117–122 (2000)Google Scholar
  28. [28]
    FENG, J. Q. A general fluid dynamic analysis of drop ejection in drop-on-demand inkjet devices. Journal of Imaging Science and Technology, 46(5), 398–408 (2002)Google Scholar
  29. [29]
    AMBRAVANESWARAN, B., WILKES, E. D., and BASARAN, O. A. Drop formation from a capillary tube: comparison of one-dimensional and two-dimensional analyses and occurrence of satellite drops. Physics of Fluids, 14(8), 2606–2621 (2002)MathSciNetzbMATHGoogle Scholar
  30. [30]
    YANG, A. S., YANG, J. C., and HONG, M. C. Droplet ejection study of a picojet printhead. Journal of Micromechanics and Microengineering, 16(1), 180–188 (2006)Google Scholar
  31. [31]
    XU, Q. and BASARAN, O. A. Computational analysis of drop-on-demand drop formation. Physics of Fluids, 19(10), 102111 (2007)zbMATHGoogle Scholar
  32. [32]
    YANG, G. and LIBURDY, J. A. Droplet formation from a pulsed vibrating micro-nozzle. Journal of Fluids and Structures, 24(4), 576–588 (2008)Google Scholar
  33. [33]
    LEIB, S. J. and GOLDSTEIN, M. E. Convective and absolute instability of a viscous liquid jet. The Physics of Fluids, 29(4), 952–954 (1986)Google Scholar
  34. [34]
    ANANTHARAMAIAH, N., TAFRESHI, H. V., and POURDEYHIMI, B. A simple expression for predicting the inlet roundness of micro-nozzles. Journal of Micromechanics and Microengineering, 17(5), 31–39 (2007)Google Scholar
  35. [35]
    LAI, J. M., HUANG, C. Y., CHEN, C. H., LINLIU, K., and LIN, J. D. Influence of liquid hydrophobicity and nozzle passage curvature on microfluidic dynamics in a drop ejection process. Journal of Micromechanics and Microengineering, 20(1), 1–14 (2010)Google Scholar
  36. [36]
    ROSELLO, M., MAITREJEAN, G., ROUX, D. C. D., JAY, R, BARBET, B., and XING, J. Influence of the nozzle shape on the breakup behavior of continuous inkjets. Journal of Fluids Engineering, 140(3), 1–8 (2017)Google Scholar
  37. [37]
    CASTREJON-PITA, J. R., MORRISON, N. F., HARLEN, O. G., MARTIN, G. D., and HUTCHINGS, I. M. Experiments and Lagrangian simulations on the formation of droplets in drop-on-demand mode. Physical Review E, 83(3), 1–12 (2011)Google Scholar
  38. [38]
    MEIXNER, R. M., CIBIS, D., KRUEGER, K., and GOEBEL, H. Characterization of polymer inks for drop-on-demand printing systems. Microsystem Technologies, 14(8), 1137–1142 (2008)Google Scholar
  39. [39]
    JANG, D., KIM, D., and MOON, J. Influence of fluid physical properties on inkjet printability. Langmuir, 25(5), 2629–2635 (2009)Google Scholar
  40. [40]
    DERBY, B. and REIS, N. Inkjet printing of highly loaded particulate suspensions. MRS Bulletin, 28(11), 815–818 (2003)Google Scholar
  41. [41]
    DERBY, B. Inkjet printing ceramics: from drops to solid. Journal of the European Ceramic Society, 31(14), 2543–2550 (2011)Google Scholar
  42. [42]
    KIM, E. and BAEK, J. Numerical study on the effects of non-dimensional parameters on drop-on-demand droplet formation dynamics and printability range in the up-scaled model. Physics of Fluids, 24(8), 082103 (2012)Google Scholar
  43. [43]
    HIRT, C. W. and NICHOLS, B. D. Volume of fluid (VOF) method for the dynamics of free boundaries. Journal of Computational Physics, 39(1), 201–225 (1981)zbMATHGoogle Scholar
  44. [44]
    BRACKBILL, J. U., KOTHE, D. B., and ZEMACH, C. A continuum method for modeling surface tension. Journal of Computational Physics, 100(2), 335–354 (1992)MathSciNetzbMATHGoogle Scholar

Copyright information

© Shanghai University and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, Beijing Innovation Center for Engineering Science and Advanced Technology, College of EngineeringPeking UniversityBeijingChina
  2. 2.National University of Sciences and Technology, H-12IslamabadPakistan
  3. 3.Center for Applied Physics and Technology, Key Laboratory of High Energy Density Physics, and Inertial Fusion Sciences and Application Collaborative Innovation Center of Ministry of EducationPeking UniversityBeijingChina

Personalised recommendations